I used D76 (or ID 11) for all pushing, as recommended by Steve Anchell in the Film Developer Cookbook. I could get results on HP5 even at 3200 with it, but highlights were blown and shadow detail scant. But the image was there.
In an updated version, he recommends XTol, which is really kinda-sorta D76 on steroids - it gives any film about a half stop gain, is sharper and has better shadow detail then D76. I tried HP5 at 1600 and it was very good indeed, and would now recommend it as an excellent choice for pushing.
Tri-X used to handle pushing better than any other film but I can't speak for the new stuff. I've tried it only at box speed, and it's not like the old Tri-X. More like a "me too" ASA 400 emulsion.
My usual developer for HP5 (my favorite film) is HC110 at 1:63, but I really don't like it as a pushing developer at any dilution for this film. Over 800, I've had consistently better results with a solvent developer.
I really thing the best answer was given above . . . . for these snapshots of friends and family, get yourself a roll of Delta 3200. The results will be better than HP5 pushed. Pushing is really just underexposing and overdeveloping, which always leads to excessive contrast and blown highights. Best to use the fastest film you can get your hands on.